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# Lecture22 - CS440/ECE448 Intro to Articial Intelligence...

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Lecture 21: Classification; Decision Trees Prof. Julia Hockenmaier [email protected] http://cs.illinois.edu/fa11/cs440 CS440/ECE448: Intro to Artificial Intelligence

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Supervised learning: classification
Supervised learning Given a set D of N items x i , each paired with an output value y i = f( x i ) , discover a function h( x ) which approximates f( x ) D = {( x 1 , y 1 ),… ( x N , y N )} Typically, the input values x are (real-valued or boolean) vectors : x i R n or x i {0,1} n The output values y are either boolean (binary classification) , elements of a finite set (multiclass classification) , or real (regression)

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The Naïve Bayes Classifier Each item has a number of attributes A 1 =a 1 ,…,A n =a n We predict the class c based on c = argmax c ! i P(A i = a i | C=c) P(C=c) 4 CS440/ECE448: Intro AI C A1 A2 An
An example Can you train a Naïve Bayes classifier to predict whether the customer wants sugar or not? What is P(coffee | sugar)? 5 CS440/ECE448: Intro AI x1 x2 Y A1: drink A2: milk? C: sugar? coffee no yes coffee yes no tea yes yes tea no no

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Decision trees
Decision trees In this example, the attributes (drink; milk?) are not conditionally independent given the class ( ʻ sugar ʼ ) 7 CS440/ECE448: Intro AI drink? milk? milk? coffee tea yes no no sugar sugar yes no sugar no sugar

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What is a decision tree? Test 2 Test 6 Test 5 Test 3 Test 4 V11 V22 V21 V12 V13 Label 2 Label 1 Label 1 test 1
Suppose I like circles that are red (I might not be aware of the rule) Features: Owner: John, Mary, Sam Size: Large, Small Shape : Triangle, Circle, Square Texture: Rough, Smooth Color: Blue, Red, Green, Yellow, Taupe Shape Triangle Circle Square Blue Red Green Yellow Taupe Color + - - - - - - ! x [Like(x) " (Circle(x) # Red(x))]

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Suppose I like circles that are red and triangles that are smooth Shape Triangle Circle Square Blue Red Green Yellow Taupe Color + - - - - - - ! x [Like(x) " ((Circle(x) # Red(x) v (Triangle(x) # Smooth(x))] texture smooth rough +
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Lecture22 - CS440/ECE448 Intro to Articial Intelligence...

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